Solve for $x$ and $y$ using elimination. $\begin{align*}6x-6y &= 4 \\ -9x-8y &= -6\end{align*}$
Explanation: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $3$ and the bottom equation by $2$ $\begin{align*}18x-18y &= 12\\ -18x-16y &= -12\end{align*}$ Add the top and bottom equations. $-34y = 0$ Divide both sides by $-34$ and reduce as necessary. $y = 0$ Substitute $0$ for $y$ in the top equation. $6x-6( 0) = 4$ $6x = 4$ $6x = 4$ $x = \dfrac{2}{3}$ The solution is $\enspace x = \dfrac{2}{3}, \enspace y = 0$.